A. Bekker

Reliability Characteristics of the Maxwell Distribution: A Bayes Estimation Study

ABSTRACT This article presents maximum likelihood, Bayes, and empirical Bayes estimators of the truncated first moment and hazard function of the Maxwell distribution. A comparison of the relative efficiency of these three estimators is performed via a Monte Carlo simulation study.

A generalization of the compound rayleigh distribution: using a bayesian method on cancer survival times

In this paper the generalized compound Rayleigh model, exhibiting flexible hazard rate, is high¬lighted. This makes it attractive for modelling survival times of patients showing characteristics of a random hazard rate. The Bayes estimators are derived for the parameters of this model and some survival time parameters from a right censored sample. This is done with respect to conjugate and discrete priors on the parameters of this model, under the squared error loss function, Varians asymmetric linear-exponential (linex) loss function and a weighted linex loss function. The future survival time of a patient is estimated under these loss functions. A Monte Carlo simu¬lation procedure is used where closed form expressions of the estimators cannot be obtained. An example illustrates the proposed estimators for this model.

Bayesian Study Of A Two-Component System With Common-Cause Shock Failures

The steady-state availability of a two-component system in series and parallel subject to individual failures (I-failures) and common-cause shock (CCS) failures is studied from a Bayesian viewpoint with different types of priors assumed for the unknown parameters in the system. Monte Carlo simulation is used to derive the posterior distribution for the steady-state availability and subsequently the highest posterior density intervals. A numerical example illustrates the results.

Bayesian multivariate normal analysis with a wishart prior

This paper considers the Bayesian analysis of the multivariate normal distribution when its covariance matrix has a Wishart prior density under the assumption of a multivariate quadratic loss function. New flexible marginal posterior distributions of the mean μ and of the covariance matrix Σ are developed and univariate cases with graphical representations are given.

Bimatrix Variate Beta Type IV Distribution: Relation to Wilks's Statistic and Bimatrix Variate Kummer-Beta Type IV Distribution

In this article, the bimatrix variate beta Type IV distribution is derived from independent Wishart distributed matrix variables. We explore specific properties of this distribution which is then used to derive the exact expressions of the densities of the product and ratio of two dependent Wilkss statistics and to define the bimatrix Kummer-beta Type IV distribution.

Bounds for the Bayes Error in Classification: A Bayesian Approach Using Discriminant Analysis

We study two of the classical bounds for the Bayes error Pe, Lissack and Fu’s separability bounds and Bhattacharyya’s bounds, in the classification of an observation into one of the two determined distributions, under the hypothesis that the prior probability χ itself has a probability distribution. The effectiveness of this distribution can be measured in terms of the ratio of two mean values. On the other hand, a discriminant analysis-based optimal classification rule allows us to derive the posterior distribution of χ, together with the related posterior bounds of Pe.

Preliminary testing of the Cobb–Douglas production function and related inferential issues

ABSTRACT In this article, we consider the multiple regression model in the presence of multicollinearity and study the performance of the preliminary test estimator (PTE) both analytically and computationally, when it is a priori suspected that some constraints may hold on the vector parameter space. The performance of the PTE is further analyzed by comparing the risk of some well-known estimators of the ridge parameter through an extensive Monte Carlo simulation study under some bounded and or asymmetric loss functions. An application of the Cobb–Douglas production function is included and from these results as well as the simulation studies, it is clear that the bounded linear exponential loss function outperforms the other loss functions across all the proposed ridge parameters by comparing the risk values.

Preliminary test and Bayes Estimation of a Location Parameter Under Blinex Loss

In this article, the preliminary test estimator is considered under the BLINEX loss function. The problem under consideration is the estimation of the location parameter from a normal distribution. The risk under the null hypothesis for the preliminary test estimator, the exact risk function for restricted maximum likelihood and approximated risk function for the unrestricted maximum likelihood estimator, are derived under BLINEX loss and the different risk structures are compared to one another both analytically and computationally. As a motivation on the use of BLINEX rather than LINEX, the risk for the preliminary test estimator under BLINEX loss is compared to the risk of the preliminary test estimator under LINEX loss and it is shown that the LINEX expected loss is higher than BLINEX expected loss. Furthermore, two feasible Bayes estimators are derived under BLINEX loss, and a feasible Bayes preliminary test estimator is defined and compared to the classical preliminary test estimator.

Subjective Bayesian Analysis of the Elliptical Model

For the multivariate elliptical model subjective Bayesian estimators of the location vector and some functions of the characteristic matrix with the normal-inverse Wishart and the normal-Wishart as prior, respectively, are derived. Fang and Li (1999) considered the elliptical model for Bayesian analysis for an objective prior structure. In addition, the newly developed results are applied to the multivariate normal- and t-distribution. A performance study is done to evaluate the normal-gamma and normal-inverse gamma distributions as suitable priors. A practical application for the posterior distributions of the multivariate t-distribution is included by means of Gibbs sampling and a Metropolis-Hastings algorithm.

On the real representation of quaternion random variables

For the first time, the matrix-variate quaternion normal and quaternion Wishart distributions are derived from first principles, that is, from their real counterparts, exposing the relations between their respective densities and characteristic functions. Applications of this theory in hypothesis testing are presented, and the density function of Wilks’ statistic is derived for quaternion Wishart matrices.